Skip to main content
SpringerLink
Log in

A spatially extended model for macroscopic spike-wave discharges

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

Spike-wave discharges are a distinctive feature of epileptic seizures. So far, they have not been reported in spatially extended neural field models. We study a space-independent version of the Amari neural field model with two competing inhibitory populations. We show that this competition leads to robust spike-wave dynamics if the inhibitory populations operate on different time-scales. The spike-wave oscillations present a fold/homoclinic type bursting. From this result we predict parameters of the extended Amari system where spike-wave oscillations produce a spatially homogeneous pattern. We propose this mechanism as a prototype of macroscopic epileptic spike-wave discharges. To our knowledge this is the first example of robust spike-wave patterns in a spatially extended neural field model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

References

  • Aicardi, J. (1988). Epileptic syndromes in childhood. Epilepsia, 29(Suppl 3), S1–5.

    Article  Google Scholar 

  • Amari, S. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biological Cybernetics, 27(2), 77–87.

    Article  PubMed  CAS  Google Scholar 

  • Amor, F., Rudrauf, D., Navarro, V., N’diaye, K., Garnero, L., Martinerie, J., et al. (2005). Imaging brain synchrony at high spatio-temporal resolution: Application to MEG signals during absence seizures. Signal Processing, 85(11), 2101–2111.

    Article  Google Scholar 

  • Asconapé, J., & Penry, J. K. (1984). Some clinical and eeg aspects of benign juvenile myoclonic epilepsy. Epilepsia, 25(1), 108–114.

    Article  PubMed  Google Scholar 

  • Bai, X., Vestal, M., Berman, R., Negishi, M., Spann, M., Vega, C., et al. (2010). Dynamic time course of typical childhood absence seizures: Eeg, behavior, and functional magnetic resonance imaging. Journal of Neuroscience, 30(17), 5884–5893.

    Article  PubMed  CAS  Google Scholar 

  • Bazhenov, M., Timofeev, I., Fröhlich, F., & Sejnowski, T. J. (2008). Cellular and network mechanisms of electrographic seizures. Drug Discovery Today. Disease models, 5(1), 45–57.

    Article  PubMed  Google Scholar 

  • Blumenfeld, H. (2005). Cellular and network mechanisms of spike-wave seizures. Epilepsia, 46(Suppl 9), 21–33.

    Article  PubMed  CAS  Google Scholar 

  • Borisyuk, R. M., & Kirillov, A. B. (1992). Bifurcation analysis of a neural network model. Biological Cybernetics, 66(4), 319–325.

    Article  PubMed  CAS  Google Scholar 

  • Breakspear, M., Roberts, J. A., Terry, J. R., Rodrigues, S., Mahant, N., & Robinson, P. A. A. (2006). Unifying explanation of primary generalized seizures through nonlinear brain modeling and bifurcation analysis. Cerebral Cortex, 16, 1296–1313.

    Article  PubMed  CAS  Google Scholar 

  • David, O., Bastin, J., Chabardes, S., Minotti, L., & Kahane, P. (2010). Studying network mechanisms using intracranial stimulation in epileptic patients. Frontiers in Systems Neuroscience, 4, 12.

    Article  Google Scholar 

  • Destexhe, A. (1998). Spike-and-wave oscillations based on the properties of GABAB receptors. Journal of Neuroscience, 18(21), 9099.

    PubMed  CAS  Google Scholar 

  • Destexhe, A., & Sejnowski, T. J. (2001). Thalamocortical assemblies. Oxford: Oxford University Press.

    Google Scholar 

  • da Silva, F. L., Blanes, W., Kalitzin, S. N., Parra, J., Suffczynski, P., & Velis, D. (2003). Epilepsies as dynamical diseases of brain systems: Basic models of the transition between normal and epileptic activity. Epilepsia, 44, 72–83.

    Article  Google Scholar 

  • Goodfellow, M., Schindler, K., & Baier, G. (2011). Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model. NeuroImage, 55(3), 920–932.

    Article  PubMed  Google Scholar 

  • Hagmann, P., Kurant, M., Gigandet, X., Thiran, P., Wedeen, V. J., Meuli, R., et al. (2007). Mapping human whole-brain structural networks with diffusion MRI. PloS ONE, 2(7), e597.

    Article  Google Scholar 

  • Holmes, M. D. (2008). Dense array EEG: Methodology and new hypothesis on epilepsy syndromes. Epilepsia, 49(Suppl 3), 3–14.

    Article  PubMed  Google Scholar 

  • Holmes, M. D., Brown, M., & Tucker, D. M. (2004). Are “generalized” seizures truly generalized? Evidence of localized mesial frontal and frontopolar discharges in absence. Epilepsia, 45(12), 1568–1579.

    Article  PubMed  Google Scholar 

  • Izhikhevich, E. (2000). Neural excitability, spiking and bursting. International Journal of Bifurcation and Chaos, 10(6), 1171–1266.

    Article  Google Scholar 

  • Jansen, B. H., & Rit, V. G. (1995). Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biological Cybernetics, 73, 357–366.

    Article  PubMed  CAS  Google Scholar 

  • Kilpatrick, Z. P., & Bressloff, P. C. (2010). Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression. Journal of Computational Neuroscience, 28(2):193–209.

    Article  PubMed  Google Scholar 

  • Marten, F., Rodrigues, S., Benjamin, O., Richardson, M. P., & Terry, J. R. (2009a). Onset of polyspike complexes in a mean-field model of human electroencephalography and its application to absence epilepsy. Philosophical Transactions of the Royal Society of London, Series A: Mathematical and Physical Sciences, 367(1891), 1145–1161.

    Article  Google Scholar 

  • Marten, F., Rodrigues, S., Suffczynski, P., Richardson P. M., & Terry, J. R. (2009b). Derivation and analysis of an ordinary differential equation mean-field model for studying clinically recorded epilepsy dynamics. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 79(2), 21911.

    Article  Google Scholar 

  • McCormick, D. A., & Contreras, D. (2001). On the cellular and network bases of epileptic seizures. Annual Review of Physiology, 63, 815–846.

    Article  PubMed  CAS  Google Scholar 

  • Meeren, H. K. M., Pijn, J. P. M., Van Luijtelaar, E. L. J. M., Coenen, A. M. L., & Lopes da Silva, F. H. (2002). Cortical focus drives widespread corticothalamic networks during spontaneous absence seizures in rats. Journal of Neuroscience, 22(4), 1480–1495.

    PubMed  CAS  Google Scholar 

  • Moeller, F., Siebner, H. R., Wolff, S., Muhle, H., Granert, O., Jansen, O., et al. (2008). Simultaneous EEG-fMRI in drug-naive children with newly diagnosed absence epilepsy. Epilepsia, 49(9), 1510–1519.

    Article  PubMed  Google Scholar 

  • Otis, T. S., & De Koninck, Y. (1993). Characterization of synaptically elicited GABAB responses using patch-clamp recordings in rat hippocampal slices. Journal of Physiology, 463, 391–407.

    PubMed  CAS  Google Scholar 

  • Robinson, P. A., Rennie, C. J., & Rowe, D. L. (2002). Dynamics of large-scale brain activity in normal arousal states and epileptic seizures. Physical Review E, 65(4), 41924.

    Article  CAS  Google Scholar 

  • Rodin, E., & Ancheta, O. (1987). Cerebral electrical fields during petit mal absences. Electroencephalography and Clinical Neurophysiology, 66(6), 457–466.

    Article  PubMed  CAS  Google Scholar 

  • Rodrigues, S., Barton, D., Marten, F., Kibuuka, M., Alarcon, G., Richardson, M. P., et al. (2010). A method for detecting false bifurcations in dynamical systems: Application to neural-field models. Biological Cybernetics, 102(2), 145–154.

    Article  PubMed  Google Scholar 

  • Rodrigues, S., Terry, J. R., & Breakspear, M. (2006). On the genesis of spike-wave oscillations in a mean-field model of human thalamic and corticothalamic dynamics. Physics Letters A, 355(4–5), 352–357.

    Article  CAS  Google Scholar 

  • Sadleir, L. G., Farrell, K., Smith, S., Connolly, M. B., & Scheffer, I. E. (2006). Electroclinical features of absence seizures in childhood absence epilepsy. Neurology, 67(3), 413–418.

    Article  PubMed  CAS  Google Scholar 

  • Stead, M., Bower, M., Brinkmann, B. H., Lee, K., Marsh, W. R., Meyer, F. B., et al. (2010). Microseizures and the spatiotemporal scales of human partial epilepsy. Brain, 133(9), 2789–2797.

    Article  PubMed  Google Scholar 

  • Stern, J. M., & Engel, J. (2005). Atlas of EEG patterns. Philadelphia: Lippincott Williams & Wilkins.

    Google Scholar 

  • Suffczynski, P., Kalitzin, S., & Lopes Da Silva, F. H. (2004). Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience, 126(2), 467–484.

    Article  PubMed  CAS  Google Scholar 

  • Thomson, A. M., & Deuchars, J. (1997). Synaptic interactions in neocortical local circuits: Dual intracellular recordings in vitro. Cerebral Cortex, 7(6), 510–522.

    Article  PubMed  CAS  Google Scholar 

  • van Luijtelaar, G., & Sitnikova, E. (2006). Global and focal aspects of absence epilepsy: The contribution of genetic models. Neuroscience and Biobehavioral Reviews, 30(7), 983–1003.

    Article  PubMed  Google Scholar 

  • Wendling, F., Bartolomei, F., Bellanger, J. J., & Chauvel, P. (2002). Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. European Journal of Neuroscience, 15(9), 1499–1508.

    Article  PubMed  CAS  Google Scholar 

  • Westmijse, I., Ossenblok, P., Gunning, B., & van Luijtelaar, G. (2009). Onset and propagation of spike and slow wave discharges in human absence epilepsy: A MEG study. Epilepsia, 50(12), 2538–2548.

    Article  PubMed  Google Scholar 

  • Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12(1), 1–24.

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgements

We thank H. Muhle, M. Siniatchkin and U. Stephani, Kiel, for clinical EEG data. We acknowledge financial support form EPSRC and BBSRC. We thank Kaspar Schindler, John Terry, Marc Goodfellow, Yujiang Wang and David Broomhead for discussion.

Author information

Authors and Affiliations

  1. Manchester Interdisciplinary Biocentre, The University of Manchester, Manchester, M1 7DN, UK

    Peter Neal Taylor & Gerold Baier

Authors
  1. Peter Neal Taylor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerold Baier
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Neal Taylor.

Additional information

Action Editor: Alain Destexhe

Source code for simulations is available at http://senselab.med.yale.edu/modeldb/.

Electronic Supplementary Material

Below is the link to the electronic supplementary material.

(PDF 19.1 KB)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Taylor, P.N., Baier, G. A spatially extended model for macroscopic spike-wave discharges. J Comput Neurosci 31, 679–684 (2011). https://doi.org/10.1007/s10827-011-0332-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-011-0332-1

Keywords

Search

Navigation